In the eighteenth century, French vestments were very much like other continental vestments, primarily focused the use of beautiful, floriated textiles. But as we start to proceed out of the eighteenth century and into the nineteenth and twentieth, we start to see a new direction which was characterized by the desire to include explicit symbolic religious imagery within the designs.
In the context of Pentecost vestments, this was of course primarily manifest by the dove which symbolizes the Holy Spirit. In the Book of Acts, chapter two, the Pentecost event is described in terms of a sound (a "mighty wind") and also flames of fire. So why then is a dove used? The answer is that in each of the four gospels the account of the Baptism of Christ tells of the Holy Spirit descending upon Christ in the form of a dove. As such, while tongues of fire have indeed appeared on Pentecost themed vestments, perhaps for reason of preferring the imagery taken from the gospels, or perhaps simply for the practical reason that a dove is much more readily recognizable and depictable (by comparison with elements like wind or fire), the dove would come to be the most popular way of depicting the Holy Spirit.
Each of today's vestments include that particular symbol and in typical French fashion, they are set into the axis of a Latin cross, and surrounded by other vegetal and floral motifs. It is in fact this combination of seventeenth and eighteenth century naturalistic motifs, with the explicit symbolism of the medieval period that makes French vestments of this particular period still so very popular today.